A bstract It is known that the't Hooft anomalies of invertible global symmetries can be
characterized by an invertible TQFT in one higher dimension. The analogous statement …

We show that the standard 1+ 1 DZ 2× Z 2 cluster model has a noninvertible global
symmetry, described by the fusion category Rep (D 8). Therefore, the cluster state is not only …

We survey recent developments in a novel kind of generalized global symmetry, the non-
invertible symmetry, in diverse spacetime dimensions. We start with several different but …

We discuss the exact non-invertible Kramers-Wannier symmetry of 1+ 1d lattice models on a
tensor product Hilbert space of qubits. This symmetry is associated with a topological defect …

Generalized symmetries often appear in the form of emergent symmetries in low energy
effective descriptions of quantum many-body systems. Non-invertible symmetries are a …

We explore exact generalized symmetries in the standard 2+ 1d lattice $\mathbb {Z} _2 $
gauge theory coupled to the Ising model, and compare them with their continuum field …

The Lieb-Schultz-Mattis (LSM) theorem provides a general constraint on quantum many-
body systems and plays a significant role in the Haldane gap phenomena and topological …

Modulated symmetries are internal symmetries that act in a non-uniform, spatially modulated
way and are generalizations of, for example, dipole symmetries. In this paper, we …

A novel interpretation of Symmetry Topological Field Theories (SymTFTs) as theories of
gravity is explored by proposing a holographic duality where the bulk SymTFT (with the …

A bstract Topological/perfectly-transmissive defects play a fundamental role in the analysis
of the symmetries of two dimensional conformal field theories (CFTs). In the present work …